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Sarnak’s Conjecture for Irregular Flows on Infinite-dimensional Torus

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Abstract

Sarnak’s Disjointness Conjecture states that the Möbius function is disjoint with any zero-entropy flow. This note establishes this conjecture, with a rate, for Furstenberg’s irregular flows on the infinite-dimensional torus.

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Acknowledgements

The author would like to thank Professors Zeng**g Chen and Jie Wu for encouragements, and the referees for their comments.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Shandong, 250100, P. R. China

    Qing Yang Liu

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  1. Qing Yang Liu
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Correspondence to Qing Yang Liu.

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Liu, Q.Y. Sarnak’s Conjecture for Irregular Flows on Infinite-dimensional Torus. Acta. Math. Sin.-English Ser. 35, 1541–1548 (2019). https://doi.org/10.1007/s10114-019-8536-9

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  • DOI: https://doi.org/10.1007/s10114-019-8536-9

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